Critical Exponents of the pure and random-field Ising models

TL;DR

This paper demonstrates that the critical exponents of the three-dimensional random-field Ising model align with those of the pure Ising model in a lower dimension, adjusted by a hyperscaling violation exponent.

Contribution

It establishes a relationship between the critical exponents of the random-field and pure Ising models through a hyperscaling violation exponent.

Findings

Critical exponents of the 3D random-field Ising model match those of the pure Ising model in 3 - theta dimensions.

The exponent theta governs hyperscaling violation in the random case.

Current estimates support the proposed dimensional relationship.

Abstract

We show that current estimates of the critical exponents of the three-dimensional random-field Ising model are in agreement with the exponents of the pure Ising system in dimension 3 - theta where theta is the exponent that governs the hyperscaling violation in the random case.